Calculates the forecast of local/moving non-parametric regression (a.k.a., LOESS, LOWESS, Savitzky–Golay filter).

## Syntax

**NxLOCREG**(**X**, **Y**, **P**, **Kernel**, **Alpha**, **Optimize**, **Target**, **Return**)

- X
- is the x-component of the input data table (a one-dimensional array of cells (e.g., rows or columns)).
- Y
- is the y-component (i.e., function) of the input data table (a one-dimensional array of cells (e.g., rows or columns)).
- P
- is the polynomial order (0 = constant, 1 = linear, 2 = Quadratic, 3 = Cubic, etc.), etc.). If missing, P = 0.
- Kernel
- is the weighting kernel function used with KNN-Regression method : 0(or missing) = Uniform, 1 = Triangular, 2 = Epanechnikov, 3 = Quartic, 4 = Triweight, 5 = Tricube, 6 = Gaussian, 7 = Cosine, 8 = Logistic, 9 = Sigmoid, 10 = Silverman.
Value Kernel 0 Uniform Kernel (default). 1 Triangular Kernel. 2 Epanechnikov Kernel. 3 Quartic Kernel. 4 Triweight Kernel. 5 Tricube Kernel. 6 Gaussian Kernel. 7 Cosine Kernel. 8 Logistic Kernel. 9 Sigmoid Kernel. 10 Silverman Kernel. - Alpha
- is the fraction of the total number (n) of data points used in each local fit (between 0 and 1). If missing or omitted, Alpha = 0.333.
- Optimize
- is a flag (True/False) for searching and using optimal bandwidth (i.e., fraction value or $\alpha$). If missing or omitted, optimize is assumed to be False.
- target
- is the desired x-value(s) to interpolate for (a single value or a one-dimensional array of cells (e.g., rows or columns)).
- Return
- is a number that determines the type of return value: 0 = Forecast (default), 1 = errors, 2 = Smoothing parameter (bandwidth), 3 = RMSE (CV). NxREG returns forecast/regression value(s) if missing or omitted.
Return Description 0 Forecast/Regression value(s) (default). 1 Forecast/Regression error(s). 2 Kernel Smoothing parameter (bandwidth). 3 RMSE (cross-validation).

## Remarks

- Local regression is a non-parametric method combining multiple regression models in a k-nearest-neighbor-based meta-model.
- Local regression or local polynomial regression (a.k.a., moving regression) is a generalization of moving average and polynomial regression.
- Its most common methods initially developed for scatterplot smoothing are LOESS (locally estimated scatterplot smoothing) and LOWESS (locally weighted scatterplot smoothing).
- Outside econometrics, LOESS is known and commonly referred to as the Savitzky–Golay filter, which was proposed 15 years before LOESS.
- $\alpha$ is called the smoothing parameter because it controls the flexibility of the LOESS regression function. Large values of ${\displaystyle \alpha }$ produce the smoothest functions that wiggle the least in response to fluctuations in the data. The smaller ${\displaystyle \alpha }$ is, the closer the regression function will conform to the data. However, using a value that is too small for the smoothing parameter is not desirable since the regression function will eventually start to capture the random error in the data.
- The number of rows of the response variable (Y) must equal the number of rows of the explanatory variable (X).
- Observations (i.e., rows) with missing values in X or Y are removed.
- NxLOCREG is related to NxKREG, but NxLOCREG uses the nearest K-NN points to calculate kernel bandwidth and conduct its local regression.
- The time series may include missing values (e.g., #N/A) at either end.
- The NxLOCREG() function is available starting with version 1.66 PARSON.

## Files Examples

## Related Links

## References

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